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Abstraction in its main sense is a conceptual process wherein general
rules Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule perta ...
and
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by sev ...
s are derived from the usage and classification of specific examples, literal ("real" or " concrete") signifiers,
first principle In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nuan ...
s, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''.
Suzanne K. Langer Susanne Katherina Langer (; ''née'' Knauth; December 20, 1895 – July 17, 1985) was an American philosopher, writer, and educator known for her theories on the influences of art on the mind. She was one of the earliest American women to achieve ...
(1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight."
Conceptual abstractions may be formed by filtering the information content of a
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by sev ...
or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a
ball A ball is a round object (usually spherical, but can sometimes be ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used fo ...
selects only the information on general ball attributes and behavior, excluding but not eliminating the other phenomenal and cognitive characteristics of that particular ball. In a
type–token distinction The type–token distinction is the difference between naming a ''class'' (type) of objects and naming the individual ''instances'' (tokens) of that class. Since each type may be exemplified by multiple tokens, there are generally more tokens than ...
, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball'). Abstraction in its secondary use is a material process,Alfred Sohn-Rethel, ''Intellectual and manual labour: A critique of epistemology'', Humanities Press, 1977 discussed in the themes below.


Origins

Thinking in abstractions is considered by
anthropologist An anthropologist is a person engaged in the practice of anthropology. Anthropology is the study of aspects of humans within past and present societies. Social anthropology, cultural anthropology and philosophical anthropology study the norms and v ...
s,
archaeologist Archaeology or archeology is the scientific study of human activity through the recovery and analysis of material culture. The archaeological record consists of artifacts, architecture, biofacts or ecofacts, sites, and cultural landscap ...
s, and sociologists to be one of the key traits in
modern human behaviour Behavioral modernity is a suite of behavioral and cognitive traits that distinguishes current ''Homo sapiens'' from other anatomically modern humans, hominins, and primates. Most scholars agree that modern human behavior can be characterized by ...
, which is believed to have developed between 50,000 and 100,000 years ago. Its development is likely to have been closely connected with the development of human language, which (whether spoken or written) appears to both involve and facilitate abstract thinking.


History

''Abstraction'' involves induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of ''specification'', which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated by Francis Bacon's ''
Novum Organum The ''Novum Organum'', fully ''Novum Organum, sive Indicia Vera de Interpretatione Naturae'' ("New organon, or true directions concerning the interpretation of nature") or ''Instaurationis Magnae, Pars II'' ("Part II of The Great Instauration ...
'' (1620), a book of modern scientific philosophy written in the late
Jacobean era The Jacobean era was the period in English and Scottish history that coincides with the reign of James VI of Scotland who also inherited the crown of England in 1603 as James I. The Jacobean era succeeds the Elizabethan era and precedes the Ca ...
Hesse, M. B. (1964), "Francis Bacon's Philosophy of Science", in A Critical History of Western Philosophy, ed. D. J. O'Connor, New York, pp. 141–52. of England to encourage modern thinkers to collect specific facts before making any generalizations. Bacon used and promoted induction as an abstraction tool; it complemented but was distinct from the ancient
deductive Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false ...
-thinking approach that had dominated the intellectual world since the times of Greek philosophers like
Thales Thales of Miletus ( ; grc-gre, Θαλῆς; ) was a Greek mathematician, astronomer, statesman, and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded him ...
,
Anaximander Anaximander (; grc-gre, Ἀναξίμανδρος ''Anaximandros''; ) was a pre-Socratic Greek philosopher who lived in Miletus,"Anaximander" in ''Chambers's Encyclopædia''. London: George Newnes, 1961, Vol. 1, p. 403. a city of Ionia (in mode ...
, and Aristotle. Thales (–546 BCE) believed that everything in the universe comes from one main substance, water. He deduced or specified from a general idea, "everything is water," to the specific forms of water such as ice, snow, fog, and rivers. Modern scientists used the approach of abstraction (going from particular facts collected into one general idea). Newton (1642–1727) derived the motion of the planets from
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulate ...
' (1473–1543) simplification, that the sun is the center of our solar system;
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
(1571–1630) compressed thousands of measurements into one expression to finally conclude that Mars moves in an elliptical orbit about the sun; Galileo (1564–1642) repeated one hundred specific experiments into the law of falling bodies.


Themes


Compression

An abstraction can be seen as a compression process, mapping multiple different pieces of
constituent Constituent or constituency may refer to: Politics * An individual voter within an electoral district, state, community, or organization * Advocacy group or constituency * Constituent assembly * Constituencies of Namibia Other meanings * Consti ...
data to a single piece of abstract data; based on similarities in the constituent data, for example, many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and " concrete". In this sense the process of abstraction entails the identification of similarities between objects, and the process of associating these objects with an abstraction (which is itself an object). :For example, '' picture 1 below'' illustrates the concrete relationship "Cat sits on Mat". Chains of abstractions can be
construe In social psychology, a construal is a way that people perceive, comprehend, and interpret their world, particularly the acts of others toward them. Researchers and theorists within virtually every sub-discipline of psychology have acknowledged the ...
d,Ross, L. (1987). The Problem of Construal in Social Inference and Social Psychology. In N. Grunberg, R.E. Nisbett, J. Singer (eds), ''A Distinctive Approach to psychological research: the influence of Stanley Schacter''. Hillsdale, NJ: Earlbaum. moving from neural impulses arising from sensory
perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system ...
to basic abstractions such as color or
shape A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. A plane shape or plane figure is constrained to lie ...
, to experiential abstractions such as a specific cat, to semantic abstractions such as the "idea" of a CAT, to classes of objects such as "mammals" and even categories such as "
object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...
" as opposed to "action". :For example, '' graph 1 below'' expresses the abstraction "agent sits on location". This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive exclusion of detail.


Instantiation

Non-existent things in any particular place and time are often seen as abstract. By contrast, instances, or members, of such an abstract thing might exist in many different places and times. Those abstract things are then said to be ''multiply instantiated'', in the sense of ''picture 1'', ''picture 2'', etc., shown
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
. It is not sufficient, however, to define ''abstract'' ideas as those that can be instantiated and to define ''abstraction'' as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and "telephone" abstract ideas since despite their varying appearances, a particular cat or a particular telephone is an instance of the concept "cat" or the concept "telephone". Although the concepts "cat" and "telephone" are ''abstractions'', they are not ''abstract'' in the sense of the objects in ''graph 1''
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
. We might look at other graphs, in a progression from ''cat'' to ''mammal'' to ''animal'', and see that ''animal'' is more abstract than ''mammal''; but on the other hand ''mammal'' is a harder idea to express, certainly in relation to '' marsupial'' or '' monotreme''. Perhaps confusingly, some
philosophies Philosophical schools of thought and philosophical movements. A Absurdism - Action, philosophy of - Actual idealism - Actualism - Advaita Vedanta - Aesthetic Realism - Aesthetics - African philosophy - Afrocentrism - Agential realism - ...
refer to '' tropes'' (instances of properties) as ''
abstract particular Abstract may refer to: * ''Abstract'' (album), 1962 album by Joe Harriott * Abstract of title a summary of the documents affecting title to parcel of land * Abstract (law), a summary of a legal document * Abstract (summary), in academic publishin ...
s''—e.g., the particular
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary ...
ness of a particular apple is an ''abstract particular''. This is similar to
qualia In philosophy of mind, qualia ( or ; singular form: quale) are defined as individual instances of subjective, conscious experience. The term ''qualia'' derives from the Latin neuter plural form (''qualia'') of the Latin adjective '' quālis'' () ...
and
sumbebekos An accident (Greek ), in metaphysics and philosophy, is a property that the entity or substance has contingently, without which the substance can still retain its identity. An accident does not affect its essence. It does not mean an "accident" as ...
.


Material process

Still retaining the primary meaning of '' or 'to draw away from', the abstraction of money, for example, works by drawing away from the particular value of things allowing completely incommensurate objects to be compared (see the section on 'Physicality' below). Karl Marx's writing on the
commodity In economics, a commodity is an economic good, usually a resource, that has full or substantial fungibility: that is, the market treats instances of the good as equivalent or nearly so with no regard to who produced them. The price of a co ...
abstraction recognizes a parallel process. The state (polity) as both concept and material practice exemplifies the two sides of this process of abstraction. Conceptually, 'the current concept of the state is an abstraction from the much more concrete early-modern use as the standing or status of the prince, his visible estates'. At the same time, materially, the 'practice of statehood is now constitutively and materially more abstract than at the time when princes ruled as the embodiment of extended power'.


Ontological status

The way that physical objects, like rocks and trees, have
being In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exi ...
differs from the way that properties of abstract concepts or relations have being, for example the way the concrete, particular, individuals pictured in '' picture 1'' exist differs from the way the concepts illustrated in '' graph 1'' exist. That difference accounts for the ontological usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that instances of them can exist, potentially in many different places and times.


Physicality

A physical object (a possible referent of a concept or word) is considered ''concrete'' (not abstract) if it is a ''particular individual'' that occupies a particular place and time. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According to , these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a
bill of lading A bill of lading () (sometimes abbreviated as B/L or BOL) is a document issued by a carrier (or their agent) to acknowledge receipt of cargo for shipment. Although the term historically related only to carriage by sea, a bill of lading may toda ...
or an accounts book. In order to avoid breaking open the containers for the count, marks were placed on the outside of the containers. These physical marks, in other words, acted as material abstractions of a materially abstract process of accounting, using conceptual abstractions (numbers) to communicate its meaning. Abstract things are sometimes defined as those things that do not exist in
reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, rea ...
or exist only as sensory experiences, like the color
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary ...
. That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like ''God'', ''the number three'', and ''goodness'' are real, abstract, or both. An approach to resolving such difficulty is to use ''
predicates Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: **Predicate (mathematical logic) ** Propositional function **Finitary relation, ...
'' as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g., ''good''). Questions about the properties of things are then
proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...
s about predicates, which propositions remain to be evaluated by the investigator. In the ''graph 1''
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
, the graphical relationships like the arrows joining boxes and ellipses might denote predicates.


Referencing and referring

Abstractions sometimes have ambiguous
referent A referent () is a person or thing to which a name – a linguistic expression or other symbol – refers. For example, in the sentence ''Mary saw me'', the referent of the word ''Mary'' is the particular person called Mary who is being spoken of ...
s. For example, " happiness" can mean experiencing various positive emotions, but can also refer to
life satisfaction Life satisfaction is a measure of a person's well-being, assessed in terms of mood, relationship satisfaction, achieved goals, self-concepts, and self-perceived ability to cope with life. Life satisfaction involves a favorable attitude towards on ...
and
subjective well-being Subjective well-being (SWB) is a self-reported measure of well-being, typically obtained by questionnaire. Ed Diener developed a tripartite model of subjective well-being in 1984, which describes how people experience the quality of their lives ...
. Likewise, "
architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings ...
" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building.


Simplification and ordering

Abstraction uses a
strategy Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the " ar ...
of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication about things in the abstract requires an intuitive or common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication. For example, many different things can be
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary ...
. Likewise, many things sit on surfaces (as in ''picture 1'', to the right). The property of ''
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary ...
ness'' and the relation '' sitting-on'' are therefore abstractions of those objects. Specifically, the conceptual diagram ''graph 1'' identifies only three boxes, two ellipses, and four arrows (and their five labels), whereas the ''picture 1'' shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph. ''Graph 1'' details some explicit relationships between the objects of the diagram. For example, the arrow between the ''agent'' and ''CAT:Elsie'' depicts an example of an '' is-a'' relationship, as does the arrow between the ''location'' and the ''MAT''. The arrows between the gerund/
present participle In linguistics, a participle () (from Latin ' a "sharing, partaking") is a nonfinite verb form that has some of the characteristics and functions of both verbs and adjectives. More narrowly, ''participle'' has been defined as "a word derived fro ...
''SITTING'' and the nouns ''agent'' and ''location'' express the diagram's basic relationship; ''"agent is SITTING on location"''; ''Elsie'' is an instance of ''CAT''. Although the description ''sitting-on'' (graph 1) is more abstract than the graphic image of a cat sitting on a mat (picture 1), the delineation of abstract things from concrete things is somewhat ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in ''
Gödel, Escher, Bach ''Gödel, Escher, Bach: an Eternal Golden Braid'', also known as ''GEB'', is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, th ...
'' (1979): An abstraction can thus encapsulate each of these levels of detail with no
loss of generality ''Without loss of generality'' (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as ''without any loss of generality'' or ''with no loss of generality'') is a frequently used expression in mathematics. The term is used to indicat ...
. But perhaps a detective or philosopher/scientist/engineer might seek to learn about something, at progressively deeper levels of detail, to solve a crime or a puzzle.


Thought processes

In philosophical terminology, ''abstraction'' is the
thought process In their most common sense, the terms thought and thinking refer to conscious cognitive processes that can happen independently of sensory stimulation. Their most paradigmatic forms are judging, reasoning, concept formation, problem solving, an ...
wherein ideas are distanced from
objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ai ...
. But an idea can be symbolized.


As used in different disciplines


In art

Typically, ''abstraction'' is used in the arts as a synonym for
abstract art Abstract art uses visual language of shape, form, color and line to create a composition which may exist with a degree of independence from visual references in the world. Western art had been, from the Renaissance up to the middle of the 19th ...
in general. Strictly speaking, it refers to art unconcerned with the literal depiction of things from the visible world—it can, however, refer to an object or image which has been distilled from the real world, or indeed, another work of art. Artwork that reshapes the natural world for expressive purposes is called abstract; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction. In the 20th century the trend toward abstraction coincided with advances in science, technology, and changes in urban life, eventually reflecting an interest in psychoanalytic theory. Later still, abstraction was manifest in more purely formal terms, such as color, freedom from objective context, and a reduction of form to basic geometric designs.


In computer science

Computer scientists Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including th ...
use abstraction to make models that can be used and re-used without having to re-write all the program code for each new application on every different type of computer. They
communicate Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inqu ...
their solutions with the computer by writing source code in some particular
computer language A computer language is a formal language used to communicate with a computer. Types of computer languages include: * Construction language – all forms of communication by which a human can specify an executable problem solution to a compu ...
which can be translated into
machine code In computer programming, machine code is any low-level programming language, consisting of machine language instructions, which are used to control a computer's central processing unit (CPU). Each instruction causes the CPU to perform a ve ...
for different types of computers to execute. Abstraction allows program designers to separate a framework (categorical concepts related to computing problems) from specific instances which implement details. This means that the program code can be written so that code doesn't have to depend on the specific details of supporting applications, operating system software, or hardware, but on a categorical concept of the solution. A solution to the problem can then be integrated into the system framework with minimal additional work. This allows programmers to take advantage of another programmer's work, while requiring only an abstract understanding of the implementation of another's work, apart from the problem that it solves.


In general semantics

Abstractions and levels of abstraction play an important role in the theory of general semantics originated by
Alfred Korzybski Alfred Habdank Skarbek Korzybski (, ; July 3, 1879 – March 1, 1950) was a Polish-American independent scholar who developed a field called general semantics, which he viewed as both distinct from, and more encompassing than, the field of se ...
.
Anatol Rapoport Anatol Rapoport ( uk, Анатолій Борисович Рапопо́рт; russian: Анато́лий Бори́сович Рапопо́рт; May 22, 1911January 20, 2007) was an American mathematical psychologist. He contributed to general ...
wrote "Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises (words)."


In history

Francis Fukuyama Francis Yoshihiro Fukuyama (; born October 27, 1952) is an American political scientist, political economist, international relations scholar and writer. Fukuyama is known for his book '' The End of History and the Last Man'' (1992), which argu ...
defines history as "a deliberate attempt of abstraction in which we separate out important from unimportant events".


In linguistics

Researchers in linguistics frequently apply abstraction so as to allow an analysis of the phenomena of language at the desired level of detail. A commonly used abstraction, the ''
phoneme In phonology and linguistics, a phoneme () is a unit of sound that can distinguish one word from another in a particular language. For example, in most dialects of English, with the notable exception of the West Midlands and the north-west ...
'', abstracts speech sounds in such a way as to neglect details that cannot serve to differentiate meaning. Other analogous kinds of abstractions (sometimes called " emic units") considered by linguists include morphemes,
grapheme In linguistics, a grapheme is the smallest functional unit of a writing system. The word ''grapheme'' is derived and the suffix ''-eme'' by analogy with ''phoneme'' and other names of emic units. The study of graphemes is called ''graphemics' ...
s, and lexemes. Abstraction also arises in the relation between syntax, semantics, and pragmatics. Pragmatics involves considerations that make reference to the user of the language; semantics considers expressions and what they denote (the
designata In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...
) abstracted from the language user; and syntax considers only the expressions themselves, abstracted from the designate.


In mathematics

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept or object, removing any dependence on real-world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. The advantages of abstraction in mathematics are: * It reveals deep connections between different areas of mathematics. * Known results in one area can suggest
conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1 ...
s in another related area. * Techniques and methods from one area can be applied to
prove Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a con ...
results in other related area. *Patterns from one mathematical object can be generalized to other similar objects in the same class. The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and might require a degree of mathematical maturity and experience before they can be assimilated.


In music

In music, the term ''abstraction'' can be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment of
tonality Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is ca ...
.
Atonal Atonality in its broadest sense is music that lacks a tonal center, or key. ''Atonality'', in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a s ...
music has no key signature, and is characterized by the exploration of internal numeric relationships.


In neurology

A recent meta-analysis suggests that the verbal system has a greater engagement with abstract concepts when the perceptual system is more engaged in processing concrete concepts. This is because abstract concepts elicit greater brain activity in the inferior frontal gyrus and middle temporal gyrus compared to concrete concepts which elicit greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus. Other research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. For example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during tool usage.


In philosophy

Abstraction in philosophy is the process (or, to some, the alleged process) in
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by sev ...
formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the
problem of universals The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: Should the properties an object has in common with other objects, such as color and shape, be considered to exist be ...
. It has also recently become popular in formal logic under
predicate abstraction In logic, predicate abstraction is the result of creating a predicate from a sentence. If Q is any formula then the predicate abstract formed from that sentence is (λy.Q), where λ is an abstraction operator and in which every occurrence of y occ ...
. Another philosophical tool for the discussion of abstraction is thought space. John Locke defined abstraction in ''
An Essay Concerning Human Understanding ''An Essay Concerning Human Understanding'' is a work by John Locke concerning the foundation of human knowledge and understanding. It first appeared in 1689 (although dated 1690) with the printed title ''An Essay Concerning Humane Understand ...
'': 'So words are used to stand as outward marks of our internal ideas, which are taken from particular things; but if every particular idea that we take in had its own special name, there would be no end to names. To prevent this, the mind makes particular ideas received from particular things become general; which it does by considering them as they are in the mind—mental appearances—separate from all other existences, and from the circumstances of real existence, such as time, place, and so on. This procedure is called abstraction. In it, an idea taken from a particular thing becomes a general representative of all of the same kind, and its name becomes a general name that is applicable to any existing thing that fits that abstract idea.' (2.11.9)


In psychology

Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist and psychoanalyst who founded analytical psychology. Jung's work has been influential in the fields of psychiatry, anthropology, archaeology, literature, philo ...
's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, different complementary psychological functions: sensation, intuition, feeling, and thinking. Together they form a structural totality of the differentiating abstraction process. Abstraction operates in one of these functions when it excludes the simultaneous influence of the other functions and other irrelevancies, such as emotion. Abstraction requires selective use of this structural split of abilities in the psyche. The opposite of abstraction is concretism. ''Abstraction'' is one of Jung's 57 definitions in Chapter XI of '' Psychological Types''.


In social theory

Social theorists deal with abstraction both as an ideational and as a material process. Alfred Sohn-Rethel (1899-1990) asked: "Can there be abstraction other than by thought?" He used the example of commodity abstraction to show that abstraction occurs in practice as people create systems of abstract exchange that extend beyond the immediate physicality of the object and yet have real and immediate consequences. This work was extended through the 'Constitutive Abstraction' approach of writers associated with the Journal ''Arena''. Two books that have taken this theme of the abstraction of social relations as an organizing process in human history are ''Nation Formation: Towards a Theory of Abstract Community'' (1996) and an associated volume published in 2006, ''Globalism, Nationalism, Tribalism: Bringing Theory Back In''. These books argue that a nation is an abstract community bringing together strangers who will never meet as such; thus constituting materially real and substantial, but abstracted and mediated relations. The books suggest that contemporary processes of globalization and mediatization have contributed to materially abstracting relations between people, with major consequences for how humans live their
lives Lives may refer to: * The plural form of a ''life'' * Lives, Iran, a village in Khuzestan Province, Iran * The number of lives in a video game * ''Parallel Lives'', aka ''Lives of the Noble Greeks and Romans'', a series of biographies of famous ...
. One can readily argue that abstraction is an elementary methodological tool in several disciplines of social science. These disciplines have definite and different concepts of "man" that highlight those aspects of man and his behaviour by idealization that are relevant for the given human science. For example, is the man as sociology abstracts and idealizes it, depicting man as a social being. Moreover, we could talk about (the man who can extend his biologically determined intelligence thanks to new technologies), or (who is simply creative). Abstraction (combined with Weberian idealization) plays a crucial role in economics - hence abstractions such as "the market" and the generalized concept of "
business Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit." Having a business name does not separa ...
". Breaking away from directly experienced reality was a common trend in 19th-century sciences (especially physics), and this was the effort which fundamentally determined the way economics tried (and still tries) to approach the economic aspects of social life. It is abstraction we meet in the case of both Newton's physics and the neoclassical theory, since the goal was to grasp the unchangeable and timeless essence of phenomena. For example, Newton created the concept of the material point by following the abstraction method so that he abstracted from the dimension and shape of any perceptible object, preserving only inertial and translational motion. Material point is the ultimate and common feature of all bodies.
Neoclassical economists Neoclassical economics is an approach to economics in which the production, consumption and valuation (pricing) of goods and services are observed as driven by the supply and demand model. According to this line of thought, the value of a good ...
created the indefinitely abstract notion of
homo economicus The term ''Homo economicus'', or economic man, is the portrayal of humans as agents who are consistently rational and narrowly self-interested, and who pursue their subjectively defined ends optimally. It is a word play on ''Homo sapiens'', u ...
by following the same procedure. Economists abstract from all individual and personal qualities in order to get to those characteristics that embody the essence of economic activity. Eventually, it is the substance of the economic man that they try to grasp. Any characteristic beyond it only disturbs the functioning of this essential core.


See also


Further reading

* * * .


References


Citations


Sources

* * Sohn-Rethel, Alfred (1977) ''Intellectual and manual labour: A critique of epistemology'', Humanities Press. * .


External links

* *
Internet Encyclopedia of Philosophy: Gottlob Frege

Discussion at The Well concerning Abstraction hierarchy
{{Authority control Concepts in epistemology Concepts in metaphilosophy Ontology Thought